Understand
It is known that every ribbon category with unimodality allows symmetrized $6j$-symbols with full tetrahedral symmetries while a spherical category does not in general.
- We give an explicit counterexample for this, namely the category $\mathcal{E}$.
- We define the mirror conjugate symmetry of $6j$-symbols instead and show that $6j$-symbols of any unitary spherical category can be normalized to have this property.
- As an application, we discuss an exactly soluble model on a honeycomb lattice.
Built on
V. Turaev; O. Viro, State sum invariants of 3-manifolds and quantum 6 j 6j -symbols , Topology 31 (1992), no. 4, 865–902
1992
Earlier work this paper cites.
V. Turaev, Quantum invariants of knots and 3-manifolds, W. de Gruyter, Berlin (1994)
1994
Earlier work this paper cites.
Similar
J. Barrett; B. Westbury, Spherical categories
1999
Cited alongside, same era.
X.-G. Wen, Quantum field theory of many-body systems, Oxford Grad. Texts (2004)
2004
Cited alongside, same era.
T. Hagge; S. Hong, Some non-braided fusion categories of rank 3 , To appear in Commun. Contemp. Math. arXiv: 0704.0208v2
Cited in the paper.
E. Rowell; R. Stong; Z. Wang, On classification of modular tensor categories , arXiv:0712.1377
Cited in the paper.
Then
M. Levin; X.-G. Wen, String-net condensation: A physical mechanism for topological phases , Phys. Rev. B71, 045110 (2005). arXiv:cond-mat/0404617v2
2005
Later among the works it cites.
2008
Later among the works it cites.
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